English

The H\"older regularity of harmonic function on bounded and unbounded p.c.f self-similar sets

Functional Analysis 2026-03-06 v2

Abstract

In this paper, we prove a generalized reverse H\"older inequality of harmonic functions on cable systems induced by post-critically finite (p.c.f.) self-similar sets. Furthermore, we also establish the H\"older regularity of harmonic functions on both bounded and unbounded p.c.f. self-similar sets, which does not involve heat kernel estimates and resistance estimates.

Keywords

Cite

@article{arxiv.2603.00659,
  title  = {The H\"older regularity of harmonic function on bounded and unbounded p.c.f self-similar sets},
  author = {Jin Gao and Yijun Song},
  journal= {arXiv preprint arXiv:2603.00659},
  year   = {2026}
}

Comments

Comments are welcome,20 pages, 5 figures